201370: [AtCoder]ARC137 A - Coprime Pair

Problem Statement

You are given integers $L,R$ ($L < R$).

Snuke is looking for a pair of integers $(x,y)$ that satisfy both of the conditions below.

• $L \leq x < y \leq R$
• $\gcd(x,y)=1$

Find the maximum possible value of $(y-x)$ in a pair that satisfies the conditions. It can be proved that at least one such pair exists under the Constraints.

Constraints

• $1 \leq L < R \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$L$ $R$

Output

Print the answer.

Sample Input 1

2 4

Sample Output 1

1

For $(x,y)=(2,4)$, we have $\gcd(x,y)=2$, which violates the condition. For $(x,y)=(2,3)$, the conditions are satisfied. Here, the value of $(y-x)$ is $1$. There is no such pair with a greater value of $(y-x)$, so the answer is $1$.

Sample Input 2

14 21

Sample Output 2

5

Sample Input 3

1 100

Sample Output 3

99